Sparse and Non-Negative BSS for Noisy Data

TL;DR

This paper introduces nGMCA, a new algorithm for non-negative blind source separation that effectively handles noisy data by leveraging sparsity and proper constraints, outperforming existing methods.

Contribution

The paper presents a novel algorithm, nGMCA, which applies proximal calculus to improve stability and robustness in non-negative sparse source separation from noisy measurements.

Findings

nGMCA outperforms state-of-the-art algorithms in noisy conditions.

The method is robust with minimal parameter tuning.

Effective on synthetic and real NMR spectra data.

Abstract

Non-negative blind source separation (BSS) has raised interest in various fields of research, as testified by the wide literature on the topic of non-negative matrix factorization (NMF). In this context, it is fundamental that the sources to be estimated present some diversity in order to be efficiently retrieved. Sparsity is known to enhance such contrast between the sources while producing very robust approaches, especially to noise. In this paper we introduce a new algorithm in order to tackle the blind separation of non-negative sparse sources from noisy measurements. We first show that sparsity and non-negativity constraints have to be carefully applied on the sought-after solution. In fact, improperly constrained solutions are unlikely to be stable and are therefore sub-optimal. The proposed algorithm, named nGMCA (non-negative Generalized Morphological Component Analysis), makes use of proximal calculus techniques to provide properly constrained solutions. The performance of nGMCA compared to other state-of-the-art algorithms is demonstrated by numerical experiments encompassing a wide variety of settings, with negligible parameter tuning. In particular, nGMCA is shown to provide robustness to noise and performs well on synthetic mixtures of real NMR spectra.